#QUOTIENT RULE CALCULUS DER PLUS#

The derivative of f of x over g of x is g of x times f prime of x minus f of x g prime of x over g of x quantity squared. This is the quotient rule and it's even better if I write it in terms of f and g, this q of x is f and g so what we're really looking at here is the derivative of f of x over g of x I'll write that this way. Now q of x times g of x let's remember that that's f of x and so we'll make the replacement when I multiply through so let's take this up here again on the left we have q prime of x and multiplying g g of x times f prime I get g of x f prime and I have a minus sign g of x times q of x as I said before that's f of x times g prime and all over, see what we have in the bottom, g of x times g of x we have the quantity g of x squared. In the top I'll have f prime times g of x or g of x times f prime and then I'll have minus q of x times g of x times g prime. Now I've solved for q prime here but I haven't quite I haven't quite finished yet because I would like my answer to be in terms only of f and g I don't want I don't want q in my answer so I'm going to have to replace q of x by f and g in a moment but before I do that I'm going to multiply the top and bottom of this equation by g of x, g of x over g of x now in the bottom that's going to give me g of x quantity squared.

#QUOTIENT RULE CALCULUS DER PLUS#

Because I already know the product rule and so I can differentiate both sides of this using the product rule now differentiating the left side gives me the first cube x times the derivative of the second g prime plus the second g of x times the derivative of the first q prime and on the right side differentiating just gives me f prime of x so in this equation since I'm looking for q prime, I need to solve for this guy here so I'm going to subtract out this term I get g of x times q prime of x equals f prime of x minus this term minus q of x oops q of x g prime of x and then I have to divide out g of x. Well let's start by representing this this relationship between q, f and g as a product so when I multiply both sides of this equation by g of x and I get q of x times g of x equals f of x this is what I'll work with here.

The quotient rule is for differentiating functions like this q of x which can be represented as a quotient of two other functions f of x over g of x so how we find q prime of x that's our goal for today. I want to talk about another really important differentiation rule called the Quotient rule.

Quotient rule calculus der